Sorry, I have misunderstood as "this is what I would do." I suppose that's a process descended from the local legal framework, then - as you say, SSN is assigned after name, and the name has some flag meaning "temporary". I would assume there's some handling in place for that eventuality.

(I have seen a different protocol: state ID number is assigned after birth, parents choose name independently of the process, the two are only linked ex post)